The equation, and the expanded equation

One equation, always true

Everything a business owns or controls — its assets — was financed by someone. Either a creditor lent the money (a liability) or the owners supplied it, by putting capital in or by leaving earnings in (equity). So at every moment:

$$\text{Assets}=\text{Liabilities}+\text{Shareholders’ equity}$$

This is not a rule that transactions are checked against; it is an identity that every transaction preserves, because every transaction is an exchange with two sides. Module 4's debits and credits are the notation that enforces it. Here you should see it hold with nothing but addition.

Worked example — Northlake's opening position

On 1 November Northlake Nordic Centre Inc. is incorporated. The same day its shareholders pay $250,000 for shares, the bank lends it $400,000, and it buys a $610,000 lodge for cash. Three exchanges, and the position after them is:

Assets:       cash 40,000 + lodge 610,000         = 650,000
Liabilities:  bank loan                            = 400,000
Equity:       650,000 − 400,000                    = 250,000

Cash is $250{,}000 + 400{,}000 - 610{,}000 = \$40{,}000$. Equity is a residual claim — the owners' interest in the assets after every creditor is paid. It is not a pile of cash. Northlake's owners have $250,000 of equity and $40,000 of cash, and the two numbers measure different things.

Expanding equity

A corporation's equity has two sources, and the balance sheet shows them separately:

$$\text{Equity}=\text{Common shares}+\text{Retained earnings}$$

Common shares is what shareholders paid in for their shares — Canadian corporations issue shares without par value, so the whole amount received sits here. Retained earnings is the income the company has earned over its life and not distributed. Northlake's $250,000 of equity is all common shares; its retained earnings on 1 November is nil. A brand-new corporation has earned nothing yet, so it has nothing retained — retained earnings only exists once income has been earned and left in, which is exactly what L3.2's operating transactions start to do.

Retained earnings itself expands once more, and this expansion is the one an exam question turns on:

$${\text{RE}}_{\text{end}}={\text{RE}}_{\text{beginning}}+\text{Net income}-\text{Dividends declared}$$

Net income raises it; a dividend declared lowers it. Note the word declared: retained earnings moves on the day the directors declare, not the day the cheques go out. And note what is not in the formula: a dividend is not an expense and never touches net income. It is a distribution of income, decided after the income is earned.

Two more positions

Kettle Creek Dental Corp. has assets of $742,000 and liabilities of $415,500. Equity = $742{,}000 - 415{,}500 = \$326{,}500$. Nothing else is needed — the residual is the definition.

Pinegrove Trail Club Inc., an older company, at its year end. Common shares $250,000;openingretainedearnings$140,000; net income for the year $58,300;dividendsdeclared$20,000. Closing retained earnings = $140{,}000 + 58{,}300 - 20{,}000 = \$178{,}300$;totalequity=$250{,}000 + 178{,}300 = \$428{,}300$. If the dividend had only been declared and not yet paid at year end, the answer is the same — and a $20,000 Dividends Payable sits among the liabilities.